Prior to fit the experimental design model by multiple linear regression, how to validate the model in terms of number of observations, orthogonality , and distance? How to evaluate the last two terms?
You can run check point batches and measure the response. Compare the predicted response with practical results. Apply suitable statistical tests.
Does that apply for all DoE approaches? If I generate 100, as example, and get the response, fit the mode, and check it. Then, should I generate more to be added for the 100 or start from the beginning?
According to Giunta et al., he presented empirical estimations to get the number of experiments in Latin Hypercube Sampling only:
1.5*V runs for 5-10 variables (V), 3*V runs for 10-20 variables (V), and 4.5*V runs for a 20- 30 variables(V).
In general, once you have a model, optimize it for what you want. Then run your process at those settings. The optimization step should tell you the mean, std err, and confidence interval for that point. If your result is within that CI, you can say your model is validated. I prefer running several different design points that are close to my optimal settings, like what Ramesh said.
You can look at "Lack of Fit" for your model. That works as a psuedo-validation of the model.
Perhaps of some interest for your query:
https://www.researchgate.net/post/how_to_explain_the_difference_between_simulation_and_experiment_result
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